Cognitive, Instructional, & Neuroimaging Factors in Math. The objective of this program project in respond to RFA HD-02-031 is to integrate investigations of the cognitive, instructional, and neurobiological factors that account for individual differences in the development of mathematical proficiencies in children with different types of learning disabilities in math. The central theme is that children vary in the degree to which they learn mathematical proficiencies and that these individual differences manifest themselves in different subtypes of math disability. To understand the sources of variability, the types must be defined and evaluated against cognitive, instructional, and neurobiological measures, and in relation to other learning and attention difficulties. The proposed program project includes four projects and three cores. Project I (Cognition) proposes to evaluate mathematical and cognitive processes that underlie the difficulties experienced by children with specific math disabilities as well as comorbid math and reading disabilities. Project II (Instruction) provides randomized controlled studies of children with only reading and comorbid reading and math disabilities, including interventions addressing of fact retrieval, procedural knowledge, and arithmetic word problems. Project III (MRI) proposes functional and structural neuroimaging studies of the subtypes of math disability evaluated in Projects I and II, specifically examining the neural correlates of these subtypes and response to intervention. Project IV (MSI) proposes magnetic source imaging studies of the subtypes evaluated in Projects I and II, also identifying the neural correlates and response to intervention with a different, but complementary functional neuroimaging modality. The cores include the Administrative Services Core (A), the Recruitment and Evaluation Core (B), and the Database and Statistics Core (C). This research program will lead to a more comprehensive classification of learning disabilities in general, a more integrated understanding of how children develop mathematical proficiencies and why some struggle, provide specific evaluations of remedial interventions, and provide important cross-discipline insights into the nature of math disabilities in children.